In this talk we will introduce the recent results about the non-linear stability of a shear layer profile for Navier-Stokes equations near a boundary. This question plays a major role in the study of the inviscid limit of Navier-Stokes equations in a bounded domain as the viscosity goes to 0. We mainly study the effect of cubic interactions on the growth of the linear instability here. In the case of the exponential profile and Blasius profile we obtain that the non-linearity tames the linear instability. We thus conjecture that small perturbations grow until they reach a magnitude O(ν1/4) only, forming small rolls in the critical layer near the boundary.
This is based on joint works with Emmanuel Grenier from Ecole Normale Superieure de Lyon, France.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
